Molecular Mechanics Calculations of the Racemization Barriers for 2,2`-Dibromo-4,4`Dicarboxybiphenyl and 2,2`-Diiodo-4,4`Dicarboxybiphenyl
Anonymous Graduate Student
[with editing by RCF]
Abstract
The racemization energy was calculated for two optically-active biphenyl derivatives using the PCModel forcefield. The results show that 2,2`-dibromo-4,4`dicarboxybiphenyl (1) and 2,2`-diiodo-4,4-dicarboxybiphenyl (2) have racemization energies of 18.60 and 22.68 kcal/mole, respectively. These values are comparable to those calculated earlier by Westheimer. The results show that the minimized structure is not planar and has a dihedral angle near 100° .
Introduction
Up until 1907 biphenyl and its derivatives were considered to have the two benzene rings as coplanar and extended. Kaufler then suggested a more or less rigid folded space formula in which the two rings are supposed to lie in planes perpendicular to the axis of the C-C single bond.1 The subsequent literature demonstrates the rapid collapse of Kauflers formula. In fact, a plethora of investigations by the great Roger Adams in the second quarter of the century demonstrated the optical activity of several biphenyl derivatives.2 The structures of biphenyl compounds have been regarded since then as the well-known, twisted, non-coplanar form.
A general theory for the racemization of optically active derivatives of biphenyl was introduced and applied by Frank Westheimer.3-4 The theory, reported in 1946,3 was similar to a general model developed independently (and almost simultaneously) by Hill for the calculation of steric strain.5 Westheimer obtained a value of 18 kcal/mol for the activation energy for the racemization of 2,2`-dibromo-4,4-dicarboxybiphenyl. The probable error was estimated to be in the order of 4 kcal/mol but not greater than 7 kcal/mol.4 Although the enthalpy of activation was at that time unknown, the free energy of activation had been determined previously as 19.5 kcal/mol.6
In this report, the results of molecular mechanics calculations of the racemization barriers are presented for 2,2`-dibromo-4,4`dicarboxybiphenyl (1) and its iodo analogue. The racemization barriers for both compounds are compared with Westheimers values.
Computational Details
The calculations were performed with the PCModel MMX forcefield, a superset of MM2. As a first approximation, the energy versus dihedral angle was plotted for both 1 and 2 using the rigid rotor approximation (ROT-E), with the rotation being about the C-C single bond connecting the two benzene rings. The dihedral angle was defined by the connected carbons and the two carbons bearing bromines, and was changed by 360° between 180° and -180° (the initial planar structure has a dihedral angle of 180°). Structures with dihedral angles which correspond to each maximum and minimum as well as an intermediate point were selected for further analysis. Geometry optimization was then performed for each of the selected structures, fixing the positions of the atoms defining the dihedral angle for each particular structure. The minimization (MMX-M) included a p -VESCF performed using the RHF Hamiltonian after an initial simple Hückel calculation.
Results
The results of the calculations for compounds 1 and 2 are summarized in Tables 1 and 2, respectively. The strain energies were plotted versus the dihedral angles for the two compounds in Figures 1 and 2, in the same order.
Table1. Results of PCModel calculations for 1.a All energy units are kcal/mol.
| Dihedral Angle a | MMX Energy kcal/mol |
Strain Energy kcal/mol |
Heat of Formation kcal/mol |
|---|---|---|---|
| 180° | 59.02 | 56.92 | -88.44 |
| 105° | 40.42 | 38.32 | -107.30 |
| 0° | 115.16 | 113.06 | -28.87 |
| 50° | 51.00 | 48.90 | -97.03 |
| 145° | 51.33 | 49.23 | -96.42 |
Table 2. Results of PCModel calculations for 2.a All energy units are kcal/mol.
| Dihedral Angle a | MMX Energy kcal/mol |
Strain Energy kcal/mol |
Heat of Formation kcal/mol |
|---|---|---|---|
| 180° | 67.04 | 64.94 | -52.26 |
| 105° | 44.36 | 42.26 | -76.78 |
| 0° | 132.08 | 129.98 | +14.69 |
| 145° | 51.23 | 49.13 | -69.72 |
Discussion
The optical activity of substituted biphenyls such as 1 and 2 occurs despite the absence of a chiral center. Adams argued that "..in any consideration of the structural conditions necessary for the existence of optical isomers, it is the asymmetric character of the molecule as a whole which is the determining factor."2 The fact that compounds 1 and 2 are asymmetric as a whole in their minimized structures (C1 point group), therefore, explains their optical activity. Hence, there are two enantiomers for each compound.
Tables 1 and 2 show that the values of the MMX energy and the strain energy are similar. Therefore, either energy can be picked to as the basis for the calculation of the racemization energy. The strain energy was arbitrarily picked in Figures 1 and 2. Meanwhile, the Tables clearly show that the heat of formation is always less negative for configurations having more strain energy, which is an expected result.
In order for racemization to take place, each enantiomer has to rotate from its dihedral angle in the direction of the other enantiomer but passing through the planar configuration. In his analysis, Westheimer considered that the planar structure acts as the activated complex for the racemization of sterically-hindered biphenyls.3 This situation can thus be visualized by an energy level diagram such as that depicted in Figure 3. Therefore, the racemization energy is represented by the energy difference between the planar structure (activated complex) and either enantiomer. This argument is supported by the results reported herein. Figures 1 and 2 show that energy maxima occur at either 0° or ± 180° with a much greater strain energy at 0°. The 0° dihedral angle corresponds to the geometry in which the steric interaction occurs between the two halides. On the other hand, angles of ± 180° represent a major steric interaction between halide atoms and hydrogen atoms. If the stereoisomer with a dihedral angle of 105° is assumed to be the S enantiomer
In view of the above discussion, the racemization energies were calculated for both 1 and 2 as the energy difference between the planar geometry and the configuration in which the dihedral angle is 105°. Based on the strain energies, the racemization energy is calculated as 18.60 kcal/mol for 1 and 22.68 kcal/mol for 2. These values are in good agreement with the corresponding values of 17.3 and 21.0 kcal/mol, respectively, as calculated by Westheimer.
The racemization energy for the iodo compound is higher than the bromo complex. In fact, all MMX and strain energies for 2 are higher for that compound (Table 2) than the corresponding energies for 1 (Table 1). Meanwhile, values of the heat of formation are less negative for the iodo compound and, indeed, the only positive heat of formation is found in Table 2 at 0° which corresponds to the greatest steric interaction between the two iodides in 2. These results are expected because iodine (Row 5 of the PT) is a much bulkier atom than bromine (Row 4).
References
